Java Programmig: Needed the most are: Recursion, Anonymous classes, and Lambda expressions. Part I: Recursion 1. If you know that, in mathematics, the Fibonacci numbers, commonly denoted F, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is, F₀ =0, F₁=1 and F_n = F_n-1 + F_n-2

The beginning of the sequence is thus: 0, 1, 1, 2, 3, 5, 8, 13, 21, ... a. Write a recursive function (method) to find the n^th number in Fibonacci sequence. b. Write an iterative function (method) to find the n^th number in Fibonacci sequence. c. Report the time elapsed by both functions in milliseconds*. The time elapsed by a function is the difference of the time reported after calling the function to the time reported before calling the function.

*To see the significant difference, try big numbers such as: 40.

Part II: Lambda Expressions 2. Suppose that a functional interface ArrayProcessor is defined as:

In the main method of a class that you create later, we defined a function that returns the length of an array of type double and used it as:

Now, using the same concept, lambda, you write and use the following functions: a. A function to find the maximum value in an array. b. A function to find the minimum value in an array. c. A function to find the sum of the values in an array. d. A function to find the average of the values in an array.

long start = System.currentTimeMillis(); // your function call long finish = System.currentTimeMillis(); long timeElapsed = finish - start; System.out.println(time Elapsed + " ms"); Fibonacci #40 using recursion function: 102334155 256 ms Fibonacci #40 using Iterative function: 102334155 ms public interface ArrayProcessor { double apply( double[] array ); double[] firstList = { 6, 2.6, 3, 5, 7, 12, 7, 2.5, 10.3, 1.7 }; Array Processor numberOfElements = (array) -> { return array.length; }; System.out.println(numberOfElements.apply(firstList)); //prints 10